Analysis of a vaccination model for carrier dependent population with a saturated incidence rate

S. K. Tiwari¹ , V. K. Gupta² , Lakhan Nagar³ , Shivram Sharma⁴

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.4 , pp.122-132, Aug-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.122132

Online published on Aug 31, 2018

Copyright © S. K. Tiwari, V. K. Gupta, Lakhan Nagar, Shivram Sharma . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This study to proposed and analyzed a vaccination model for carrier dependent population with a saturated incidence rate. The equilibrium’s for the model are found and their stability investigated. Gives the numerical examples in support of results

Key-Words / Index Term :
carrier dependent, vaccination, environmental discharge, infectious diseases, carrying capacity.

References :
[1] D. Greenhalth, “some results for an SEIR epidemic model with density dependence in the death rate”, IMA J. Math. Appl. Med Biol., 9, 67-106, 1992.
[2] F. Bereszovsky, G. Karev, B. Song, C. Castillo-Chavez,” A simple epidemic model with surprising dynamics”, Math. Biosc. Engg., 2(1), 133-152, 2005.
[3] G.S. Harold, “Household and stored food insects of public health importance”, US Department of Health, Education and Welfare, Communicable Disease Center, Atlanta, GA, 1960.
[4] H.W. Hethcote, “Qualitative analysis of communicable disease models”, Math. Biosc., 28, 335-356, 1976.
[5] J. Zhou, H.W. Hethcote, “Population size dependent incidence in models for diseases without immunity”, J. Math. Biol. 32, 809–834,1994.
[6] K.L. Cooke,” Stability Analysis for a vector Disease model”, Rocky Mountain J. Math., 9, 31-42, 1979.
[7] L.Q. Gao, H.W. Hethcote, “Disease transmission model with density dependence demographics”, J. Math. Biol. 32,717-731, 1992.
[8] L.Esteva , M. Matias, “A model for vector transmitted diseases with saturation incidence”, J. Biol. Sys., 9(4), 235-245, 2001.
[9] M. Ghosh, P. Chandra, P. Sinha, J.B. Sukla, “An Epidemiological model for carrier dependent infectious diseases with environmental effect”, Int. J. Appl. Sc. Comp., 7, 188-204, 2000.
[10] M. Ghosh, P. Chandra, P. Sinha, J.B. Sukla, “Modeling the spread of carrier dependent infectious disease with environmental effects”,Appl. Math. Comp., 152, 385-402, 2004.
[11] M. Ghosh, P.Chandra, P. Sinha, J.B. Sukla,” Modeling the spread of bacterial disease: effect of service providers from an environmentally degraded region”, Appl. Math. Comp., 160, 615-647, 2005.
[12] N.T.J. Bailey, “Spatial models in the epidemiology of infectious diseases”, Lecture Notes in Biomathematics, 38,233-261,1980.
[13] P. Das, D. Mukharjee, A. K. Sarkar, “Study of carrier dependent infectious disease cholera”, J. Biol. Sys., 13(3),233-244, 2005.
[14] S. Hsu, A.. Zee,” Global spread of infectious diseases”, J. Bio. Sys., 12, 289-300, 2004.
[15] S. Singh, P. Chandra, J.B. Sukla, “Modelling and analysis of the spread of carrier dependent infectious diseases with environmental effects”, J. Biol. Sys.,11(3), 325-335, 2003.